拟增生算子方程的广义最速下降逼近的收敛性

倪仁兴

应用数学学报 ›› 2009, Vol. 32 ›› Issue (1) : 143-153.

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PDF(328 KB)
应用数学学报 ›› 2009, Vol. 32 ›› Issue (1) : 143-153. DOI: 10.12387/C2009015
论文

拟增生算子方程的广义最速下降逼近的收敛性

    倪仁兴
作者信息 +

Convergence of Generalized Steepest Descent Approximation to Quasi-accretive Operators Equations

    NI Renxing
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文章历史 +

摘要

证明了广义最速下降逼近强收敛于定义在一致光滑实Banach 空间的真子集上的局部有界拟增生算子的零点的一充要条件, 相关的结果处理含φ-强拟增生算子的非线性方程 迭代解的收敛性. 所得的结果推广和统一如Xu和Roach, Xu、Zhang和Roach, Chidume, Zegeye和Ntatin, 徐宗本和蒋耀林, Chidume, Zhou等人的相应结果.

Abstract

A necessary and sufficient condition is proved for a generalized steepest descent approximation to converge to the zeros of quasi-accretive locally bounded operators defined on proper subsets of uniformly smooth real Banach space. Related results deal with the strongly convergence of the scheme to a solution of equations involving φ-strongly quasi-accretive operators. These results extend and unify corresponding ones by Xu and Roach, Xu Zhongben and Jiang Yaolin, Chidume, Xu, Zhang and Roach, Zhou and others.

关键词

拟增生算子 / φ-强增生算子 / 广义最速下降逼近 / 一致光滑实Banach空间 / 局部有界算子 / 充要条件

Key words

quasi-accretive operator / φ-strongly quasi-accretive operator / generalized steepest descent approximation / uniformly smooth real Banach space / locally bounded operator / necessary and sufficient condition

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导出引用
倪仁兴. 拟增生算子方程的广义最速下降逼近的收敛性. 应用数学学报, 2009, 32(1): 143-153 https://doi.org/10.12387/C2009015
NI Renxing. Convergence of Generalized Steepest Descent Approximation to Quasi-accretive Operators Equations. Acta Mathematicae Applicatae Sinica, 2009, 32(1): 143-153 https://doi.org/10.12387/C2009015
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